If cost = -0.42 and cosw = -0.80, both t and w are positive, and the angles determined by t and w are in quadrant 3, then which of the following statements is true?
Here is my answer (B)....
a. t > w
B. w > t(X)
c. Cannot be determined
please explain why I got it wrong and correct it for me. Thank you.
To determine the relationship between t and w, we can compare the values of cosw and cost.
We are given that cosw = -0.80 and cost = -0.42. Since cosw is negative, we know that the angle determined by w is in quadrant 2 or quadrant 3. Since cost is also negative, we know that the angle determined by t is also in quadrant 2 or quadrant 3.
Since both angles are in quadrant 3, we can conclude that both t and w are positive.
Now, let's compare the values of cosw and cost:
cosw = -0.80
cost = -0.42
Since -0.80 is smaller than -0.42, we can conclude that cosw is smaller than cost.
Therefore, w is greater than t.
Hence, the correct answer is not B, but rather A: t > w.
You got the answer wrong because of the incorrect interpretation of the given information. The statement "w > t" is true based on the given information. Let me explain:
In quadrant 3, both t and w are positive. Since cosw = -0.80, which is negative, w must be an obtuse angle (between 90 degrees and 180 degrees).
On the other hand, since cost = -0.42, which is also negative, t must be an acute angle (between 0 degrees and 90 degrees).
So, based on the given information, w is larger than t. Therefore, the correct statement is: "w > t" (not "t > w").
Let me know if you need any further clarification!